[Paleopsych] Sigma XI: Storied Theory
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Thu Jul 21 20:52:14 UTC 2005
see full issue: July-August 2005
Volume: 93 Number: 4 Page: 308
Science and stories are not only compatible, they're inseparable, as shown
by Einstein's classic 1905 paper on the photoelectric effect
Science seems to be afraid of storytelling, perhaps because it
associates narrative with long, untestable yarns. Stories are
perceived as "just" literature. Worse, stories are not reducible to
mathematics, so they are unlikely to impress our peers.
This fear is misplaced for two reasons. First, in paradigmatic
science, hypotheses have to be crafted. What are alternative
hypotheses but competing narratives? Invent them as fancifully as you
can. Sure, they ought to avoid explicit violations of reality (such as
light acting like a particle when everyone knows it's a wave?), but
censor those stories lightly. There is time for experiment--by you or
others--to discover which story holds up better.
The second reason not to fear a story is that human beings do science.
A person must decide what molecule is made, what instrument built to
measure what property. Yes, there are facts to begin with, facts to
build on. But facts are mute. They generate neither the desire to
understand, nor appeals for the patronage that science requires, nor
the judgment to do A instead of B, nor the will to overcome a
seemingly insuperable failure. Actions, small or large, are taken at a
certain time by human beings--who are living out a story.
Better Theory Through Stories
One might think that experiments are more sympathetic than theories to
storytelling, because an experiment has a natural chronology and an
overcoming of obstacles (see my article, "Narrative," in the
July-August 2000 American Scientist). However, I think that narrative
is indivisibly fused with the theoretical enterprise, for several
One, scientific theories are inherently explanatory. In mathematics
it's fine to trace the consequences of changing assumptions just for
the fun of it. In physics or chemistry, by contrast, one often
constructs a theoretical framework to explain a strange experimental
finding. In the act of explaining something, we shape a story. So C
exists because A leads to B leads to C--and not D.
Two, theory is inventive. This statement is certainly true for
chemistry, which today is more about synthesis than analysis and more
about creation than discovery. As Anne Poduska, a graduate student in
my group, pointed out to me, "theory has a greater opportunity to be
fanciful, because you can make up molecules that don't (yet) exist."
Three, theory often provides a single account of how the world
works--which is what a story is. In general, theoretical papers do not
lay out several hypotheses. They take one and, using a set of
mathematical mappings and proof techniques, trace out the
consequences. Theories are world-making.
Finally, comparing theory with experiment provides a natural ending.
There is a beginning to any theory--some facts, some hypotheses. After
setting the stage, developing the readers' interest, engaging them in
the fundamental conflict, there is the moment of (often experimental)
truth: Will it work? And if that test of truth is not at hand, perhaps
the future holds it.
The theorist who restates a problem without touching on an
experimental result of some consequence, or who throws out too many
unverifiable predictions, will lose credibility and, like a
long-winded raconteur, the attention of his or her audience. Coming
back to real ground after soaring on mathematical wings gives theory a
Let me analyze a theoretical paper to show how this storytelling
imperative works. Not just any paper, but a classic appropriate to the
centennial of Albert Einstein's great 1905 papers.
The Puzzle of Dwarvish Work
Einstein's paper on the photoelectric effect, published that fecund
year, was singled out by the 1921 Nobel Committee (late as usual, and
perhaps still afraid of relativity) as the basis for their award. It
is also the only one of the 1905 papers that Einstein himself deemed
revolutionary. But when one reads the article, the photoelectric
effect appears late, as a denouement; the paper begins elsewhere.
The unwritten prologue is the contemporary interest in black-body
radiation--the tendency of any object, no matter what its composition,
to radiate light when it is heated. We see it in iron nestled in the
forge, glowing red, then yellow, then white.
The intensity of this emitted light varies with the color
(wavelength). At low temperatures, bodies radiate in the infrared. As
the temperature rises, the maximum intensity of the radiated light
moves into the red, then extends through the spectrum to the
ultraviolet. At high temperatures, objects radiate intense light
across the visible spectrum--that's white heat. The intensity of
radiated light diminishes in the extreme ultraviolet and far infrared
(see right). Astronomers estimate the temperatures of stars from just
The standard (and eminently successful) understanding of light in
Einstein's day came from James Maxwell's electromagnetic theory.
Coupled with thermodynamics and the kinetic theory of gases--a high
expression of Newtonian mechanics--electromagnetic theory led to a
"radiation law" that described how the intensity of light varied with
wavelength at each temperature. The law fit the data--at long
wavelengths. At short wavelengths, the equation derived from
electromagnetic theory failed, in what became known as "the
In 1900, Max Planck found an expression that fit over the entire range
of observations. Planck further perceived that his accurate radiation
law could be obtained only if the energies of the little bits of
oscillating charge that caused the light (he called them "resonators")
assumed discontinuous values. So the quantum was born.
Planck had trouble believing that physics was, deep down,
discontinuous. He spent many years searching for a way around what he
discovered. But that is another story.
How Einstein Tells It
The photoelectric paper is modestly entitled, "On a Heuristic Point of
View Concerning the Production and Transformation of Light." Einstein
begins by stating the problem posed by the quantum hypothesis: He
defines the resonators as bound electrons and takes us, with
characteristic clarity, made possible by five years of experience with
quanta, through Planck's derivation. He develops the characters in his
tale--the radiation, Planck, his resonators, classical electromagnetic
Then Einstein does something new. He sets out to derive Planck's
radiation law without any assumptions about how light is generated.
How does he do that? By assigning an entropy (the measure of
randomness, a concept already in wide use by then) to the light and
relating that entropy to the density of the radiation. Einstein proves
that the entropy of the light in the black body varies with volume
just the way that entropy varies with volume for that standby of
freshman chemistry, the ideal gas.
This demonstration is direct. It's not Hemingway, but for scientific
prose, really exciting. Einstein is taking us somewhere--we don't know
where yet, but by the way he sets the scene, by his pace and
conviction, we know something is going to happen.
Pretty incredible. No resonators, just a functional analogy of atoms
or molecules to light. Playing out the analogy, light of a given
wavelength could be described as if its energy came in dollops of
what Einstein called Rbv/N, and today we would call hv, a constant (h)
times the light's frequency (v). But that's just a way of looking at
things--it's not for nothing that Einstein put the word heuristic in
the title. Or is it? When do stories become real?
Back to the paper: Einstein has just rederived Planck's radiation law
without resonators. Yet the discreteness of the light's energy, its
quantization, is newly manifest in Einstein's work. There is no
mistaking it. From this climax the paper cruises along another
plateau, then swoops into a breathtaking shift of scene. Philipp
Lenard had three years earlier observed "cathode rays," or beams of
electrons, by shining light onto a metal. The phenomenon happened only
when the frequency of that light exceeded a certain minimum; below
that frequency (or above that wavelength)--nothing. After seeing the
electrons, Lenard observed that their kinetic energy depended on the
color of the light, their number on the intensity of the light.
This phenomenon we now call the photoelectric effect. Aside from being
today a primary source of information on molecules and surfaces, the
effect is behind photoelectric cells opening elevator doors, and is
used in solar cells and light-sensitive diodes.
Back to 1905. Einstein just says: Let's assume light is quantized in
units of hv, and that a "light quantum" (we would call it a photon
today) gives up all its energy to a single electron. The electron
needs a certain energy to leave the surface; if it has some left over,
the extra contributes to its motion. Einstein calculates, in a couple
of terse sentences, the energies involved and finds reasonable
agreement with Lenard's measurements. With this and another
calculation on the ionization of gases, he brings us down to
Except reality is not down, it is evidence. Evidence that this story
of light being quantized is not just any story. This one is worth
telling to our great-grandchildren.
Einstein's theory leaves us soaring, thinking what else this strange,
discontinuous view of light might explain. Soon Bohr will use it to
give us the first theory of an atom. This story is as exciting as
Thomas Mann's 1902 Buddenbrooks, which Einstein might have been
reading at the time.
The photoelectric paper was submitted to Annalen der Physik (Annals of
Physics) in March 1905. But Planck's quantum theory, and the nature of
light, had been on Einstein's mind for quite a while. On April 30,
1901 he wrote to his future wife, Mileva Maric, "I came recently on
the idea that when light is generated, perhaps there occurs a direct
conversion of kinetic energy to light. Because of the parallelism:
motional energy of the molecules--absolute temperature--spectrum
(energy of radiation in equilibrium). Who knows when a tunnel will be
dug through these hard mountains!"
The Story Is in the Theory
All theories tell a story. They have a beginning, in which people and
ideas, models, molecules and governing equations take the stage. Their
roles are defined; there is a puzzle to solve. Einstein sets his
characters into motion so ingeniously, using entropy to tease out the
parallels between moving molecules and the energy of light. The story
develops; there are consequences of Einstein's approach. And at the
end, his view of light as quantized and particular confronts the
reality of the heretofore unexplained photoelectric effect. The
postscripted future, of all else that can be understood and all new
things that can be made, is implicit.
Perceptive reader Anne Poduska notes that the photoelectric paper "is
particularly interesting because of the layering of perspectives
(similar to legends being passed from one generation to the next, with
each storyteller adding their own flair/details)." Indeed, Einstein
uses Planck's development of the radiation law even as the younger
physicist claims he will do it differently. He parlays belief in the
discreteness of molecules (some of his contemporaries still doubted
their existence) into an argument, first cautious, then growing in
strength, of the discreteness of light.
A young man of 25, Einstein had mastered the old stories. In this
paper he combined the ways others looked at the world, and trusting
analogy as much as mathematics, made something new. Science is an
inspired account of the struggle by human beings to understand the
world. Changing it in the process. How could this be anything but a
Thanks to Anne Poduska for her careful reading and suggestions.
* Cassidy, D. 2005. Einstein and the quantum hypothesis. Annalen der
Physik (series X) 14 (supplement):15-22.
* Einstein, A. 1905. Über einen die Erzeugung und Verwandlung des
Lichtes betreffenden heuristischen Gesichtpunkt. Annalen der
Physik (series IV) 17:132-148. An English translation may be found
in Ter Haar, D. 1967. The Old Quantum Theory. New York: Pergamon,
and on the web at
* Kuhn, T. S. 1978. Black-Body Theory and the Quantum Discontinuity,
1894-1912. New York: Oxford University Press.
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